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Mathematics
Problem
Let
f
:
R
→
R
f:\mathbb R\to\mathbb R
f
:
R
→
R
be given by
f
(
x
)
=
3
x
+
2
f(x)=3x+2
f
(
x
)
=
3
x
+
2
and
g
:
R
→
R
g:\mathbb R\to\mathbb R
g
:
R
→
R
by
g
(
x
)
=
x
3
−
1
g(x)=x^{3}-1
g
(
x
)
=
x
3
−
1
. The expression for
(
g
∘
f
)
−
1
(
y
)
(g\circ f)^{-1}(y)
(
g
∘
f
)
−
1
(
y
)
is a)
y
−
1
3
+
2
3
\dfrac{\sqrt[3]{y-1}+2}{3}
3
3
y
−
1
+
2
b)
y
+
1
3
−
2
3
\dfrac{\sqrt[3]{y+1}-2}{3}
3
3
y
+
1
−
2
c)
y
3
−
2
3
\dfrac{\sqrt[3]{y}-2}{3}
3
3
y
−
2
d)
3
y
+
1
3
−
2
3\sqrt[3]{y+1}-2
3
3
y
+
1
−
2
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